Twenty-First Century Quantum Mechanics: Hilbert Space to Quantum Computers

Mathematical Methods and Conceptual Foundations

  • Guido Fano
  • S M Blinder

Part of the UNITEXT for Physics book series (UNITEXTPH)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Guido Fano, S. M. Blinder
    Pages 1-41
  3. Guido Fano, S. M. Blinder
    Pages 43-84
  4. Guido Fano, S. M. Blinder
    Pages 85-120
  5. Guido Fano, S. M. Blinder
    Pages 153-193
  6. Guido Fano, S. M. Blinder
    Pages 195-262
  7. Back Matter
    Pages 263-271

About this book


This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result. This book will be of interest to a wide readership seeking to understand modern quantum mechanics and its potential applications.


fundamental concepts of Quantum Mechanic for non-specialist mathematical aspects of quantum mechanics Quantum computation Heisenberg uncertainty principle Schrödinger equation Hidden variables Spin of elementary particles Isotropic vectors Quantum entanglement Bell’s inequality Measurement and decoherence Quantum cryptography

Authors and affiliations

  • Guido Fano
    • 1
  • S M Blinder
    • 2
  1. 1.Dipartimento di Fisica e AstronomiaUniversità di BolognaBolognaItaly
  2. 2.University of MichiganAnn ArborUSA

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-58731-8
  • Online ISBN 978-3-319-58732-5
  • Series Print ISSN 2198-7882
  • Series Online ISSN 2198-7890
  • Buy this book on publisher's site
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